The CFA states that the Portfolio Sharpe Ratio Squared = Benchmark Sharpe Ratio Squared + Information Ratio Squared. I don’t understand how this equation can hold if cash and leverage is introduced because it is also stated that Sharpe ratio is not affected by cash/leverage while information ratio is.
Then if cash is included, information ratio is changed, shouldn’t portfolio Sharpe ratio squared also change as a result of the equation above too?
I would appreciate it if someone can point out where I went wrong in my thinking, thanks!